The irony of small town life being more interesting than outsiders would assume.
This is an implicit argument in the narrative, but basically, by featuring all the small connections between the citizens of Mariposa, Leacock shows a rich ecosystem of interconnected characters. This leads to small melodramas at every turn, so much so that humor and levity are essential parts of making sense of it all.
Religion is ironically oriented.
Instead of Christianity being shown for its virtuous support of the congregation or charity for the lower class, we are shown a stressed out reverend, Dean Rupert Drone, whose main issue is that his new church building left the church with a lot of debt, which will likely mean asking people for money. Basically, the irony is that Christianity is founded on the ideas of charity and giving money away, and the minister here is in the most need of all of them.
The irony of humor in small town life.
These stories might seem like dramas, but they're closer to comedy. By taking a humorous point of view, the narrator manages to show the town as rich and fascinating, whereas without that humor, the town might seem complicated and tedious. This highlights the value of levity in small towns.
The irony of romance, or 'looking in the wrong place.'
Look at Zena Pepperleigh. Peter Pupkin loves her and wants to be with her, but ironically, Zena doesn't seem to notice or isn't interested, choosing her romantic novels instead. The irony is fairly clear, but basically, Zena would rather entertain herself with romance than do the hard work of finding it. Also, it's a small town, so every suitor counts.
The irony of the undertaker.
Golgotha Gingham is a funny name, because Golgotha is the 'Place of the Skull,' where Jesus Christ was crucified. This is because Gingham is the undertaker, but ironically, it seems this mortician cares more about the dead than the living.